Neighborinos (12 pt.) homer simpson and ned flanders can both contribute to mowing the grass between their properties. let q denote the total number of minutes spent on mowing in a given week, where qh is the sum of minutes spent mowing by homer and by flanders, respectively homer's demand curve is q for q50 50- pн () for q > 50 flanders' demand curve is 10 -q for q < 20 pr(q) = for q> 20 the marginal cost of mowing is the opportunity cost of time, which will change throughout the problem depending on how busy each neighbor is in a given week a. (3 pt.) calculate the social marginal benefit curve as a function of q. (hint: it's a "kinked" or piecewise-linear curve, so you'll need two equations to describe it: one for smaller values of q and one for larger values of q. you may want to draw a graph.) b. (3 pt.) suppose that the marginal cost of mowing is 70 for each neighbor. what is the socially optimal total amount of mowing, q,? if homer and flanders play a static game, what are the nash equilibrium quant ities q and qf? c. (3 pt.) now suppose the marginal cost is 45 for each neighbor. what is the socially optimal total amount of mowing, q.? from the standpoint of pareto efficiency, does it matter who does the mowing (and if so, which neighbor should do the mowing)? if homer and flanders play a static game, what are the nash equilibrium quantities qf and q? d. (3 pt.) finally, suppose that homer's marginal cost is 20, while flanders's marginal cost is only 5. what is the socially optimal amount q4? from the standpoint of pareto efficiency, does it matter who does the mowing (and if so, which neighbor should do the mowing)? what are the nash equilibrium quantit ies qji and qf?